Problem: Graph this system of equations and solve. $7x-5y = -10$ $-4x+10y = -30$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $7x-5y = -10$ , to slope-intercept form. $y = \dfrac{7}{5} x + 2$ The y-intercept for the first equation is $2$ , so the first line must pass through the point $(0, 2)$ The slope for the first equation is $\dfrac{7}{5}$ . Remember that the slope tells you rise over run. So in this case for every $7$ positions you move up You must also move $5$ positions to the right. $5$ positions to the right. $7$ positions up from $(0, 2)$ is $(5, 9)$ Graph the blue line so it passes through $(0, 2)$ and $(5, 9)$ Convert the second equation, $-4x+10y = -30$ , to slope-intercept form. $y = \dfrac{2}{5} x - 3$ The y-intercept for the second equation is $-3$ , so the second line must pass through the point $(0, -3)$ The slope for the second equation is $\dfrac{2}{5}$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move up You must also move $5$ positions to the right. $5$ positions to the right. $2$ positions up from $(0, -3)$ is $(5, -1)$ Graph the green line so it passes through $(0, -3)$ and $(5, -1)$ The solution is the point where the two lines intersect. The lines intersect at $(-5, -5)$.